Abstract

In this study, we introduce the concepts of fuzzy subalgebras and fuzzy ideals in TM-algebras and investigate some of its properties. Problem statement: Let X be a TM-algebra, S be a sub algebra of X and I be a p-ideal of X. Let µ and v be fuzzy sets in a TM-algebra X. Approach: Define the upper level subset µt of µ and the cartesian product of µ and v from X×X to [0,1] by minimum of µ (x) and v (y) for all elements (x, y) in X×X. Result: We proved any subalgebra of a TM-algebra X can be realized as a level subalgebra of some fuzzy subalgebra of X and µt is a p-ideal of X. Also we proved, the cartesian product of µ and v is a fuzzy p-ideal of X×X. Conclusion: In this article, we have fuzzified the subalgebra and ideal of TM-algebras into fuzzy subalgrbra and fuzzy ideal of TM-algebras. It has been observed that the TM-algebra satisfy the various conditions stated in the BCC/ BCK algebras. These concepts can further be generalized.

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